BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Butter Chicken

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 304
Joined: Wed Jan 27, 2010 8:35 am
Location: International Space Station
Thanked: 11 times
Followed by:3 members

Butter Chicken

by Aman verma » Tue Feb 23, 2010 3:36 am
Q: Barack Singh Lamba, a famous cook in Capitol Hills ,Washington D.C, is known for his gourmet Indian food.The Food Quality control department once set on an inspection to check the quality of the food at Barack's restaurant.The food inspector took four different samples of Butter Chicken, an Indian delicacy , each sample containing a single piece of chicken.The inspector measured the weights of the pieces of chickens in all possible pairs.The weight obtained are 59gm, 61gm, 62gm, 63gm , 64gm and 66 gm. The weight of the lightest(least weight) piece of chicken is :

a)27gm.

b)28gm.

c)29gm.

d)30gm.

e)31gm.
800. Arjun's-Bird-Eye
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Tue Feb 23, 2010 4:07 am
Aman verma wrote:Q: Barack Singh Lamba, a famous cook in Capitol Hills ,Washington D.C, is known for his gourmet Indian food.The Food Quality control department once set on an inspection to check the quality of the food at Barack's restaurant.The food inspector took four different samples of Butter Chicken, an Indian delicacy , each sample containing a single piece of chicken.The inspector measured the weights of the pieces of chickens in all possible pairs.The weight obtained are 59gm, 61gm, 62gm, 63gm , 64gm and 66 gm. The weight of the lightest(least weight) piece of chicken is :

a)27gm.

b)28gm.

c)29gm.

d)30gm.

e)31gm.
Let p, q, r, s are the weights such that p < q < r < s, then the possible pairings are p + q, p + r, p + s, q + r, q + s, and r + s, and it must be an ascending order, logically. The so obtained weights are also given in the same order. If it is so, then p + q = 59, p + r = 61, p + s = 62, q + r = 63, q + s = 64, and r + s = 66. A bit of algebra, like add p + q = 59, p + r = 61, to get 2 p + q + r = 120, but q + r = 63, hence 2 p = 57 or p = 28.5; and all choices for the least weight piece of chicken are integers. If the question reads "four different samples of Butter Chicken", aren't we supposed to take them different weight-wise here, in a question about weights only?

What's the OA and source?
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 102
Joined: Sat Feb 20, 2010 5:38 am
Location: IIM Ahmedabad
Thanked: 10 times

by firdaus117 » Tue Feb 23, 2010 4:09 am
Let,the weights be w1,w2,.........w4;w1 being lightest and w4 being heaviest.
Given w1+w2=59 w1+w3=61 w2+w4=64 w3+w4=66
Hence,w3-w2=2 w4-w1=5
Of the two remaining weights viz 62 and 63,one is w1+w4 and another is w2+w3.
Let w1+w4=62
2w1=57
w1=28.5 not in options Rejected
Now,w1+w4=63
2w1=58
or, w1=29
Optionc
Let me give the disclaimer here:
This question has two sets of solution both true,29 30 32 34 and 28.5,30.5,32.5,33.5.
So,W1 can both be 28.5 or 29.Only because 28.5 is not among options,I chose 29. :D
Top
User avatar
Legendary Member
Posts: 1275
Joined: Thu Sep 21, 2006 11:13 pm
Location: Arabian Sea
Thanked: 125 times
Followed by:2 members

by ajith » Tue Feb 23, 2010 5:00 am
Aman verma wrote:Q: Barack Singh Lamba, a famous cook in Capitol Hills ,Washington D.C, is known for his gourmet Indian food.The Food Quality control department once set on an inspection to check the quality of the food at Barack's restaurant.The food inspector took four different samples of Butter Chicken, an Indian delicacy , each sample containing a single piece of chicken.The inspector measured the weights of the pieces of chickens in all possible pairs.The weight obtained are 59gm, 61gm, 62gm, 63gm , 64gm and 66 gm. The weight of the lightest(least weight) piece of chicken is :

a)27gm.

b)28gm.

c)29gm.

d)30gm.

e)31gm.
Since there are 6 different combinations possible, there should be 4 different pieces

let us call them a, b, c, d

say a is the lightest piece, b is the second lightest piece c second heaviest and d the heaviest

a+b = 59 --(1)
c+d = 66 ---(2)
a+c =61----(3)
b+d = 64
c+b =62 (or a+d =62)
a+d = 63---(6) (or b+c= 63)


if I add all of these equations I get 3(a+b+c+d) = 375 ; (a+b+c+d)= 125 --(7)
(7) - ((1)+(3)) => d-a = 4

a+d =62
a-d = -4

a = 29

(we can get a value of a =28.5 if we solve the alternate equations)
Always borrow money from a pessimist, he doesn't expect to be paid back.
Top
Legendary Member
Posts: 610
Joined: Fri Jan 15, 2010 12:33 am
Thanked: 47 times
Followed by:2 members

by kstv » Tue Feb 23, 2010 8:33 am
Taking cue from Ajith and answer choices.
The different ways of arranging the different weights are 4C2 i.e 6 ways - already given.
Let a, b, c & d be the weights in ascending order. Lighest is a and heaviest is d.
a+b= 59 and c+d = 66 logic being the lighest piece has to be in 59 while the heaviest has to be in 66.
At this point we can rule out option d) 30 gm and e) 31 as the lighest.
leaving 27,28, 29.
a = 27 b = 32 a+b = 59, a+c = 61 then c = 34 but c+d = 66 d= 32 going nowhere
a= 28 b = 31 a+c = 61 then c = 33 but c +d = 66 d = 33 not possible
a = 29 b = 30 a+c = 61 then c = 32 but c+d = 66 then d = 34 , this works
Top
Master | Next Rank: 500 Posts
Posts: 304
Joined: Wed Jan 27, 2010 8:35 am
Location: International Space Station
Thanked: 11 times
Followed by:3 members

by Aman verma » Wed Feb 24, 2010 5:55 am
Wallaaah !! [spoiler]c) 29[/spoiler] it is. Even I didn't had such an efficient method for solving this problem. I was amazed by Ajith's and Firdaus117's method of solving this problem. With my method I would have solved this in 12-15 minutes:-too time consuming.Thanks to all of you for suggesting such short cut methods.A simpler method is always preferable over a complex method of solving.
800. Arjun's-Bird-Eye
Top
Post new topic Post Reply
• Page 1 of 1